1 / 20

Analyzing Data from Small N Designs using Multilevel Models

Analyzing Data from Small N Designs using Multilevel Models. Eden Nagler The Graduate Center, CUNY David Rindskopf, Ph.D The Graduate Center, CUNY. Overview/Intro. What is our current work? Where did we start? How does HLM fit into this framework?. 2 Initial Datasets:.

erling
Télécharger la présentation

Analyzing Data from Small N Designs using Multilevel Models

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Analyzing Data from Small N Designs using Multilevel Models Eden Nagler The Graduate Center, CUNY David Rindskopf, Ph.D The Graduate Center, CUNY

  2. Overview/Intro • What is our current work? • Where did we start? • How does HLM fit into this framework?

  3. 2 Initial Datasets: Stuart, R.B. (1967). Behavioral control of overeating. Behavior Research & Therapy, 5, (357-365). Dicarlo, C.F. & Reid, D.H. (2004). Increasing pretend toy play of toddlers with disabilities in an inclusive setting. Journal of Applied Behavior Analysis, 37(2), (197-207).

  4. Stuart (1967):

  5. Stuart (1967):Procedures for Getting data into HLM

  6. Stuart (1967): Procedures for Getting data into HLM

  7. Stuart (1967): Level-1 dataset

  8. Stuart (1967): Level-2 dataset

  9. Stuart (1967): HLM (Linear model) Linear Model: POUNDS = π0 + π1*(MONTHS12) + e

  10. Stuart (1967): HLM – Linear Model Estimates Final estimation of fixed effects: Standard Approx. Fixed Effect Coefficient Error T-ratio d.f. P-value ---------------------------------------------------------- For INTRCPT1,P0 INTRCPT2, B00 156.439560 5.053645 30.956 7 0.000 For MONTHS12 slope, P1 INTRCPT2, B10 -3.078984 0.233772 13.171 7 0.000 ---------------------------------------------------------- The outcome variable is POUNDS ---------------------------------------------------------- POUNDSij ≈ 156.4 – 3.1*(MONTHS12) + eij

  11. Stuart (1967): HLM – Quadratic Model Quadratic Model: POUNDS = π0+ π1*(MONTHS12)+ π2*(MON12SQ)+e

  12. Stuart (1967): HLM – Quadratic Model Estimates Final estimation of fixed effects: Standard Approx. Fixed Effect Coefficient Error T-ratio d.f. P-value ----------------------------------------------------------- For INTRCPT1, P0 INTRCPT2, B00 158.833791 5.321806 29.846 7 0.000 For MONTHS12 slope, P1 INTRCPT2, B10 -1.773039 0.358651 -4.944 7 0.001 For MON12SQ slope, P2 INTRCPT2, B20 0.108829 0.021467 5.070 7 0.001 ----------------------------------------------------------- The outcome variable is POUNDS ----------------------------------------------------------- POUNDSij ≈ 158.8 – 1.8(MONTHS12) + 0.1*(MON12SQ) + eij

  13. Stuart (1967): HLM – Linear vs. Quadratic Model Stuart (1967) – Actual Data Linear Model Prediction Quadratic Model Prediction

  14. Dicarlo & Reid (2004):

  15. Dicarlo & Reid (2004): Level-1 dataset

  16. Dicarlo & Reid (2004): Level-2 dataset

  17. Dicarlo & Reid (2004): HLM – Simple Model Simple Model: FREQRND = π 0 + π1*(PHASE) + e

  18. Dicarlo & Reid (2004): HLM – Simple Model Estimates Level-1 Model Level-2 Model log[L] = P0 + P1*(PHASE) P0 = B00 + R0 P1 = B10 + R1 ---------------------------------------------------------- Final estimation of fixed effects: (Unit-specific model) Standard Approx. Fixed Effect Coefficient Error T-ratio d.f. P-value ---------------------------------------------------------- For INTRCPT1,P0 INTRCPT2, B00 -0.769384 0.634548 -1.212 4 0.292 For PHASE slope,P1 INTRCPT2, B10 2.516446 0.278095 9.049 4 0.000 ---------------------------------------------------------- LN(FREQRNDij) = -0.77 + 2.52*(PHASE) + eij

  19. Dicarlo & Reid (2004): HLM – Simple Model Estimates LOG(FREQRNDij) = B00 + B10*(PHASE) + eij For PHASE=0 (BASELINE): LOG(FREQRNDij) = B00 FREQRNDij= exp(B00) For PHASE=1 (TREATMENT): LOG(FREQRNDij) = B00 + B10 FREQRNDij= exp(B00+B10) = exp(B00)*exp(B10) Estimates: B00 = -0.77; B10 = 2.52 For PHASE=0 (BASELINE): FREQRNDij= exp(B00) = exp(-0.77) = 0.46 For PHASE=1 (TREATMENT): FREQRNDij= exp(B00+B10) = exp(-0.77+2.52) = exp(1.75) = 5.75

  20. In conclusion… • Other issues we’ve encountered and explored • Issues we’ve encountered, but not yet explored • Issues we’ve not yet encountered nor explored

More Related